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Derivative of Some Standard Functions

if x belongs ...

Question

if x belongs to (pi\2,3pi\2)value of tan^-1(tanX)

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{tan}^{- 1} (cot x) + {cot}^{- 1} (tan x)

0 < x < \frac{π}{2}

y = {tan}^{- 1} (cot x) + {cot}^{- 1} (tan x),

\frac{d y}{d x}

{tan}^{- 1} (cot x) + {cot}^{- 1} (tan x) =

______. (where,

0 < x < \frac{π}{2})

.

3 \cdot {tan}^{- 1} x = {tan}^{- 1} (\frac{3 x - x^{3}}{1 - 3 x^{2}})

x

{[{tan}^{- 1} x]}^{2} - 2 [{tan}^{- 1} x] + 1 \leq 0

[.]

denotes greatest integer

\leq x, x

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